Method for estimating wind

ABSTRACT

Attitude, ground velocity, and acceleration inputs from an aircraft Inertial Navigation System (INS) and/or a Global Positioning System (GPS) instrument on board the aircraft, are used to estimate wind velocity relative to the aircraft and/or the ground in three dimensions. A wind velocity in the third dimension is assumed to be zero. In an exemplary embodiment of the invention, one or more of a) atmospheric density, b) speed of sound, c) air temperature, d) thrust of the aircraft, e) aerodynamic force coefficients of the aircraft, and f) mass of the aircraft, are used in conjunction with the inputs from the INS/GPS instrument(s) to estimate the wind velocity. Air temperature can be used, for example, together with an ambient air pressure and/or a known altitude of the aircraft to indicate an atmospheric density.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The invention relates generally to the field of aeronauticalnavigation, and in particular to estimation of wind velocity.

[0003] 2. Background Information

[0004] A need exists to accurately, efficiently and economicallyestimate wind velocity relative to an aircraft and/or the ground usingoutputs from an Inertial Navigation System (INS) and/or a GlobalPositioning System (GPS) instrument on board the aircraft.

SUMMARY OF THE INVENTION

[0005] In accordance with an exemplary embodiment of the invention, amethod for estimating a velocity of a fluid (e.g., air) in threedimensions relative to a first object (e.g., an aircraft) in the fluidand/or relative to a second object (e.g., the earth or an object infixed position relative to the earth), includes determining anacceleration of the first object relative to the second object. Themethod further includes determining a dynamic pressure of the fluid onthe first object, determining a thrust vector of the first objectrelative to the second object, and determining the velocity of the fluidrelative to the second object in the three dimensions, based on thedetermined acceleration, the determined dynamic pressure, the determinedthrust vector and an assumption that a speed of the fluid along thethird dimension is nominally zero.

[0006] In accordance with another exemplary embodiment of the invention,a method for estimating air velocity of a vehicle includes determining aparameter associated with the vehicle, determining a weighting factor toweight each equation in the equation set, based on the determinedparameter, and solving the weighted equation set to estimate the airvelocity of the vehicle.

[0007] In accordance with exemplary embodiments of the invention, theattitude, ground velocity, and acceleration inputs from an aircraftInertial Navigation System (INS) and/or a Global Positioning System(GPS) instrument on board the aircraft, are used to estimate windvelocity relative to the aircraft and/or the ground in three dimensions.In an exemplary embodiment of the invention, one or more of a)atmospheric density, b) speed of sound, c) air temperature, d) thrust ofthe aircraft, e) aerodynamic force coefficients of the aircraft, and f)mass of the aircraft, are used in conjunction with the inputs from theINS/GPS instrument(s) to estimate the wind velocity. Air temperature canbe used, for example, together with an ambient air pressure and/or aknown altitude of the aircraft to indicate an atmospheric density.

[0008] The estimate of wind velocity can be desirable, for example, tohelp an autopilot keep the aircraft stable and guide the aircraft to adestination or waypoint, and to estimate pitch and yaw of the aircraftrelative to the airmass through which it is moving. The estimate of windvelocity can also be used to determine an aerial dispense point offree-falling submunitions so that the submunitions will arrive with adesired accuracy and/or pattern at a target or target zone.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Other objects and advantages of the present invention will becomeapparent to those skilled in the art from the following detaileddescription of preferred embodiments, when read in conjunction with theaccompanying drawings wherein like elements have been designated withlike reference numerals and wherein:

[0010]FIG. 1 shows a flow diagram of an exemplary embodiment of thepresent invention.

[0011]FIG. 2 shows features of an exemplary embodiment of the invention.

[0012]FIG. 3 shows a block diagram of an exemplary embodiment of theinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013]FIG. 1 shows a flow diagram of an exemplary embodiment of thepresent invention. In a first step 102, an acceleration of a firstobject, for example an aircraft, is determined relative to a secondobject, for example the earth or an object in fixed position relative tothe earth. This can be done using, for example, an Inertial NavigationSystem (INS) on board the aircraft, and/or a Global Positioning System(GPS) instrument that indicates the aircraft's position (including, forexample, orientation) relative to the earth. In a second step 104, adynamic pressure of a fluid (for example, air) on the first object isdetermined.

[0014] In a next step 106, a thrust vector of the first object relativeto the second object is determined. This can be determined, for example,based on the first object's position and orientation relative to thesecond object, and on a known thrust vector relative to the firstobject. For example, the thrust vector of an aircraft's jet turbineengine with respect to the aircraft, can be known based on the design ofthe aircraft. For example, the direction of engine thrust relative tothe aircraft nose is determined by design of the aircraft and istherefore known. This knowledge together with knowledge of the aircraftattitude indicates the thrust vector. Some aircraft can vary theirthrust vector, for example the Harrier jet aircraft and the YF-23 jetaircraft. For those aircraft, control signals or settings for directingthe thrust vector and/or feedback sensors such as nozzle positionsensors can indicate the thrust vector relative to the aircraft nose.

[0015] In a next step 108, the velocity of the fluid is determinedrelative to the second object (and/or the first object, since velocityand position/orientation of the first object relative to the secondobjection is known) based on several factors. The factors include thedetermined acceleration of the first object relative to the secondobject, the determined dynamic pressure of the fluid on the firstobject, the determined thrust vector of the first object, and anassumption that a speed of the fluid along the third dimension is zero.In an exemplary embodiment of the invention, the third dimension isvertical, for example aligned parallel to or coaxial with the earth'sgravitational force.

[0016]FIG. 2 shows exemplary features in accordance with anotherembodiment of the invention. In step 202, the velocity of the fluid isdetermined by solving an over-constrained set of equations, where theequation set is a combination of force equations and the third componentof the speed of the fluid (which is zero), and the solution is obtainedvia a weighted least squares fit.

[0017] In a next step 204, the weighting of the least squares fit isadjusted based on a probability that the velocity of the fluid in oralong the third dimension is zero. Specifically, as the assumption thatthe velocity of the fluid along the third dimension is zero becomes lesscertain, the weighting is adjusted to increase influence of the forceequations on the solution, and decrease influence of the velocityequation on the solution.

[0018] In step 206, the converse situation is addressed. When thecertainty of the assumption increases, the weighting is adjusted toincrease influence of the velocity equation and decrease influence ofthe force equations.

[0019] Generally speaking, the probability that the wind or airmass hasa vertical velocity increases the closer one comes to the earth'ssurface. This occurs, for example, because topographical variations(e.g., mountains and hills) and thermographic variations of the earth'ssurface affect movement and behavior of the air. Accordingly, in anexemplary embodiment of the invention the weighting can be adjusted as afunction of the aircraft's altitude above mean sea level, or on analtitude above ground level. The weighting can also be adjusted based onlateral speed of the air over the earth's surface, because the speed atwhich an airmass moves over the earth's surface (e.g., over mountainousareas and/or into another airmass having a different temperature) ofteninfluences the vertical movement or speed of the airmass. Various modelsor estimations of a vertical velocity of the airmass through which theaircraft is moving, can be used separately or together with otherfactors regarding vertical air movement to influence or adjust theweighting of the force equations vs. the velocity equation.

[0020] Specifically, the features of the invention described above canbe realized using the equations and mathematical relationships describedbelow.

[0021] Wind velocity can be estimated, for example at an aircraft during“trim aero” conditions. This estimated wind velocity can be combinedwith a ground velocity of the aircraft to calculate a velocity of theaircraft relative to the airmass through which it is moving. The windvelocity can also be used to calculate pitch angle of attack alpha (α),yaw angle of attack beta (β), and total velocity or Mach number. Forexample, the wind velocity can be estimated at a low rate, during trimaero conditions, and then the estimated wind velocity can be used tocompute total velocity, alpha and beta at a higher rate.

[0022] Alpha (α) refers to pitch angle of attack of the aircraftrelative to the airmass, or in other words whether the air is comingfrom above or below the nose of the aircraft, or straight at the nose ofthe aircraft in the pitch plane. Beta (β) refers to yaw angle of attackof the aircraft relative to the airmass, or in other words whether theair is coming from the left or right side of the aircraft nose, orstraight at the nose of the aircraft in the yaw plane. Thus Betaindicates whether the aircraft is flying sideways through the airmass.When the aircraft is flying in a trim aero condition, the aircraft isflying with a fixed pitch angle of attack Alpha (α) and a fixed yawangle of attack Beta (β).

[0023] The wind velocity can be estimated using the following fourequations. $\begin{matrix}{F_{x} = {{T_{x} - {q \cdot s \cdot C_{A}} - {m \cdot a_{x}}} = 0}} & (1) \\{F_{y} = {{T_{y} + {q \cdot s \cdot C_{Y}} - {m \cdot a_{y}}} = 0}} & (2) \\{F_{z} = {{T_{z} - {q \cdot s \cdot C_{N}} - {m \cdot a_{z}}} = 0}} & (3) \\{W_{D} = 0} & (4)\end{matrix}$

[0024] In Equations (1-4), T is the thrust from the thrust model, and qis dynamic pressure. More specifically, q is a scalar, is equal to$\frac{\rho \cdot v^{2}}{2},$

[0025] and is pressure due to velocity of the aircraft with respect tothe air mass through which it moves. In accordance with an exemplaryembodiment of the invention, q is not measured directly, but is computedby estimating air density (ρ) and subtracting estimated wind velocityfrom known ground speed velocity. (Ground speed can be known, forexample, based on information provided by an inertial navigation systemonboard the aircraft).

[0026] Also in Equations (1-4) s is the reference area (which is thearea of the aircraft body normal to the velocity vector at zero angle ofattack), m is mass of the object, W_(D) is the down component orvertical movement component of the wind (i.e., indicating zero velocityalong the third dimension), and C_(A), C_(y), C_(N) are aerodynamiccoefficients. The A, Y and N subscripts represent body coordinates.Specifically, C_(A) is the axial force coefficient, C_(y) is the sideforce coefficient, and C_(N) is the normal force coefficient.

[0027] Where the aircraft has a turbine jet engine, a thrust output ofthe engine can be estimated based on a speed of the engine, i.e. the RPM(revolutions per minute) of the engine. In exemplary embodiments of theinvention, other parameters can be used alone or in various combinationsto determine or estimate thrust output. Parameters can include a) engineparameters, b) thrust element parameters, and atmospheric parameters.Exemplary engine parameters for a turbine engine can include enginespeed, rate of fuel consumption, temperatures at various locations inthe turbine engine, and other parameters that indicate a power output ofthe engine. Exemplary engine parameters for a piston engine can includeengine speed, throttle setting, manifold pressure, rate of fuelconsumption, ignition timing, and so forth. Those skilled in the artwill recognize that for other engine types such as rocket engines,parameters appropriate to that engine type can be measured and analyzedto provide an indication of power output and generated thrust. Thrustelements can include propellers for piston engines, fans and/orpropellers for turbine engines, and so forth. The speed of the thrustelement(s) and where applicable the angle of propeller or fan blades,can also be evaluated to estimate or determine thrust. With respect toatmospheric parameters, air density and temperature can be used toevaluate or determine power output of the motor, and efficiency of thethrust element(s). In an exemplary embodiment of the invention, enginespeed is used as a simple measure of output thrust. In another exemplaryembodiment of the invention, engine speed is mapped to an output thrustcurve based on a set of standard or expected conditions or parametervalues (fuel flow, air density & temperature, etc.). Alternatively, twoor more parameters such as engine speed and air density can be mapped toan output thrust curve based on a set of standard or expected conditionsor values of other parameters (fuel flow, blade angle, etc.).

[0028] The set of Equations (1-4) can be solved using a weighted leastsquares fit. This can be done, for example, by proceeding formally inthe following fashion. First, write the Equations (1-4) as a vectorequation $\begin{matrix}{{{F\left( {{q(W)},{c_{i}(W)}} \right)} = 0}{{Then},}} & (5) \\{{{{F\left( W_{true} \right)} \approx {{F\left( W_{est} \right)} + {\frac{\partial F}{\partial W}\left\lbrack {W_{true} - W_{est}} \right\rbrack}}} = 0}{and}} & (6) \\\begin{matrix}{\frac{\partial F}{\partial W} = {{\frac{\partial F}{\partial Q} \cdot \frac{\partial q}{\partial V_{total}} \cdot \frac{\partial V_{total}}{\partial W}} +}} \\{{{\frac{\partial F}{\partial C_{N}} \cdot \left( {{\frac{\partial C_{N}}{\partial V_{total}} \cdot \frac{\partial V_{total}}{\partial W}} + {\frac{\partial C_{N}}{\partial\alpha} \cdot \frac{\partial\alpha}{\partial W}} + {\frac{\partial C_{N}}{\partial\beta} \cdot \frac{\partial\beta}{\partial W}}} \right)} +}} \\{{{\frac{\partial F}{\partial C_{Y}} \cdot \left( {{\frac{\partial C_{Y}}{\partial V_{total}} \cdot \frac{\partial V_{total}}{\partial W}} + {\frac{\partial C_{Y}}{\partial\alpha} \cdot \frac{\partial\alpha}{\partial W}} + {\frac{\partial C_{Y}}{\partial\beta} \cdot \frac{\partial\beta}{\partial W}}} \right)} +}} \\{{\frac{\partial F}{\partial C_{A}} \cdot \left( {{\frac{\partial C_{A}}{\partial V_{total}} \cdot \frac{\partial V_{total}}{\partial W}} + {\frac{\partial C_{A}}{\partial\alpha} \cdot \frac{\partial\alpha}{\partial W}} + {\frac{\partial C_{A}}{\partial\beta} \cdot \frac{\partial\beta}{\partial W}}} \right)}}\end{matrix} & (7)\end{matrix}$

[0029] In accordance with an exemplary embodiment of the invention, thepartials for$\frac{\partial C_{N}}{\partial V},\frac{\partial C_{N}}{\partial\alpha},\frac{\partial C_{N}}{\partial\beta},\frac{\partial C_{Y}}{\partial V},\frac{\partial C_{Y}}{\partial\alpha},\frac{\partial C_{Y}}{\partial\beta},\frac{\partial C_{A}}{\partial V},\frac{\partial C_{A}}{\partial\alpha},\frac{\partial C_{A}}{\partial\beta},{{etc}.},$

[0030] can be computed numerically by multiple entries into trim aerodata tables. The trim aero data tables can simply by multipledimensioned tables for each aero coefficient. The data for a coefficientcan be stored in more than one table, for example one can have a nominalC_(N) table as a function of alpha, beta and mach, and aC_(N—)correction which could be a function of, for example, an enginespeed of the aircraft. The arrangement of these tables can be a strictfunction of an interpolation routine used to look up the data. Forexample, a typical table format for a variable or coefficient C(x,y,z)would be L, M, N, x(1), x(2) . . . , x(L), y(1), y(2) . . . , y(M),z(1), z(2) . . . , z(N), C(x(1, y(1), z(1)), . . . , C(x(L), y(M),z(N)).

[0031] In other words, in accordance with an exemplary embodiment of theinvention, the coefficients C_(A), C_(Y), C_(N) are stored in tables,and an iterative approach is used to solve the over-determined equations1-4. A Gauss-Newton technique can be used, which requires the partialderivatives of the coefficients with respect to mach, alpha and beta(see equation 7). These derivatives can be obtained numerically by usingmultiple entries from the trim aero data tables and an interpolationroutine to compute values between the entries. Other methods canalternatively be used, for example a nonlinear search method, a geneticalgorithm, simulated annealing, and so forth as those skilled in the artwill appreciate. The important thing is that the equations (1-4) areoverdetermined (four equations, with three unknown wind velocitycomponents). Alpha, beta and mach can be determined if the aircraftattitude, ground velocity, and the wind velocity are known, given someassumptions such as knowledge or predictions regarding atmosphericconditions. In exemplary embodiment of the invention, an altitude of theaircraft is used to generate nominal atmospheric parameters, and ameasured air temperature is used to correct nominal air density andvelocity of sound through the air.

[0032] Returning to our analysis, since there are four equations andthree unknowns, the equations may be solved by a weighted least squaresfit. Writing [εW]=[W_(true)−W_(est)], the equations to be solved are

[0033] where σ_(I) represents the four weightings of each equation. Asthose skilled in the art will recognize, the ratio of the fourweightings is important, rather than the specific value of eachweighting. Using a Penrose pseudoinverse yields $\begin{matrix}{{\left\lbrack {\varepsilon \quad W} \right\rbrack = {\lbrack G\rbrack \begin{bmatrix}{T_{x} - {q \cdot S \cdot C_{A}} - {m \cdot a_{x}}} \\{T_{y} + {q \cdot S \cdot C_{Y}} - {m \cdot a_{y}}} \\{T_{z} - {q \cdot S \cdot C_{N}} - {m \cdot a_{z}}} \\{- W_{D}}\end{bmatrix}}}\quad {where}} & (9) \\{G = {\left\lbrack {\left( {\left\lbrack \frac{1}{\sigma_{I}} \right\rbrack \cdot \left\lbrack \frac{\partial F}{\partial W} \right\rbrack} \right)^{T} \cdot \left\lbrack \frac{1}{\sigma_{I}} \right\rbrack \cdot \left\lbrack \frac{\partial F}{\partial W} \right\rbrack} \right\rbrack^{- 1} \cdot \left( {\left\lbrack \frac{1}{\sigma_{I}} \right\rbrack \cdot \left\lbrack \frac{\partial F}{\partial W} \right\rbrack} \right)^{T} \cdot \left\lbrack \frac{1}{\sigma_{I}} \right\rbrack}} & (10)\end{matrix}$

[0034] The updated wind estimate is

[W]=[W]+[εW]  (11)

[0035] Total velocity with respect to wind is

[V _(T)]^(NED) =[V _(E)]^(NED) +[W] ^(NED)   (12)

[0036] where [V_(E)]^(NED) is from the Inertial Navigation System, and“NED” refers to North-East-Down coordinates, i.e., earth coordinates.This can also be expressed in Body coordinates, i.e., from the referenceframe of a vehicle in the airmass (front-back, left-right, up-down), inthe following fashion. $\begin{matrix}{{\left\lbrack V_{T} \right\rbrack^{Body} = {C_{NED}^{Body} \cdot \left\lbrack V_{T} \right\rbrack^{NED}}}{{where}\quad C_{NED}^{Body}}} & (13)\end{matrix}$

[0037] is a mathematical transformation from NED to Body coordinates.

[0038] In accordance with an exemplary embodiment of the invention, thismathematical transformation is performed by the Inertial NavigationSystem.

[0039] Computation of α and β can be performed in the following fashion,where $\begin{matrix}{{\alpha = {a\quad {\tan \left( \frac{\left\lbrack V_{T} \right\rbrack^{z - {body}}}{\left\lbrack V_{T} \right\rbrack^{x - {body}}} \right)}}}{and}} & (14) \\{\beta = {a\quad {\sin \left( \frac{\left\lbrack V_{T} \right\rbrack^{y - {body}}}{\left\lbrack V_{T} \right\rbrack } \right)}}} & (15)\end{matrix}$

[0040] In summary, the technique of constraining the wind velocity inthe third dimension to be nominally zero in the set of force equations(1-3) via the equation (4), produces an over-determined set of equationswhose contributions to the wind estimate and/or the pitch angle ofattack, yaw angle of attack and airspeed triad of variables may becontrolled by adjusting the weight, σ_(I), assigned to each of theequations. This method or technique can also be performed using aniterated measurement Kalman filter implementation. Computationoperations of the method can for example be performed by a digitalmicroprocessor or computer system, located for example on board theaircraft, and can be performed by one or more computing machine(s)(digital or analog) working separately or together. In an exemplaryembodiment of the invention, a fresh wind velocity estimate is generatedevery tenth of a second, i.e., at a rate of 10 hertz. In otherembodiments the wind velocity is estimated at different rates, fasterand/or slower than 10 hertz, based on the available computing power andon the requirements of the particular application or use of the windestimate.

[0041] In addition, in accordance with an exemplary embodiment of theinvention and based on the principles described above, the wind can beestimated using lift, drag and aerodynamic roll angle, where theaccelerometer data are rotated through the angles of attack, which arebeing estimated.

[0042]FIG. 3 shows a block diagram of an exemplary embodiment of theinvention, capable of performing the various functions described above.Specifically, FIG. 3 shows an Inertial Navigation System 302 and aGlobal Positioning System 304 connected to a processor 310 to provideposition information of an aircraft relative to an object such as theearth. Those skilled in the art will appreciate that the positioninformation can indicate an attitude or orientation of the aircraftrelative to the object, as well as distance information. Those skilledin the art will also appreciate that the processor 310 can determinevelocity and acceleration information by analyzing changes in theposition information over time.

[0043]FIG. 3 also shows an Engine Thrust System 308 connected to provideengine thrust information, or information necessary for the processor310 to determine output thrust of the aircraft's engine or motor, suchas motor speed or any of the parameters described further above withrespect to output thrust. The Engine Thrust System 308 can comprise, forexample, connections to engine control and/or monitoring instrumentsthat provide information signals which the processor 310 can use. TheSystem 308 can also include engine control and/or monitoringinstruments.

[0044]FIG. 3 also shows an atmospheric sensor package 306 connected toprovide atmospheric information to the processor 310. The atmosphericinformation can include, for example, air temperature at or near theaircraft, ambient air pressure at or near the aircraft, and so forth.The atmospheric information can be obtained by sensors onboard theaircraft. Alternatively, the atmospheric information can be obtained bysensors not on board the aircraft and then transmitted by atelecommunication link to the processor 310. In a preferred embodiment,the link is a wireless link. The processor 310 can be located on boardthe aircraft. Alternatively, the processor 310 can be located off boardthe aircraft at a location remote from the aircraft. In that caseposition information and any other necessary information originating onthe aircraft would be transmitted to the processor 310 by atelecommunications link, and the resulting wind estimate output by theprocessor 310 would then be transmitted or otherwise conveyed to thepilot and/or autopilot of the aircraft. Those skilled in the art willrecognize that exemplary aircraft can be remotely piloted. Those skilledin the art will also recognize that the processor 310 can be implementedas a digital microprocessor or computer system or as an analog computer,and can be implemented as two or more computing machines (digital oranalog) working separately or together, at the same or differentphysical locations.

[0045] It will be appreciated by those skilled in the art that thepresent invention can be embodied in other specific forms withoutdeparting from the spirit or essential characteristics thereof, and thatthe invention is not limited to the specific embodiments describedherein. The presently disclosed embodiments are therefore considered inall respects to be illustrative and not restrictive. The scope of theinvention is indicated by the appended claims rather than the foregoingdescription, and all changes that come within the meaning and range andequivalents thereof are intended to be embraced therein.

1. A method for estimating, at a first object in a fluid, a velocity ofthe fluid relative to a second object, comprising: determining anacceleration of the first object relative to the second object;determining a dynamic pressure of the fluid on the first object;determining a thrust vector of the first object relative to the secondobject; and determining the velocity of the fluid relative to the secondobject in the three dimensions, based on the determined acceleration,the determined dynamic pressure, the determined thrust vector and anassumption that a speed of the fluid along a single dimension andrelative to the second object is zero.
 2. The method of claim 1, whereinthe step of determining the velocity of the fluid comprises: combiningforce equations and a velocity equation to form an over-constrained setof equations, wherein the velocity equation indicates an assumed zerospeed of the fluid along the third dimension relative to the secondobject, and the force equations include the determined acceleration, thedetermined dynamic pressure, and the determined thrust vector.
 3. Themethod of claim 2, wherein the step of determining the velocity of thefluid comprises: solving the over-constrained set of equations via aweighted least squares fit, wherein the weighting determines relativeinfluence of the force equations versus the velocity equation on thefluid velocity estimate.
 4. The method of claim 3, comprising: adjustingthe weighting to increase influence of the velocity equation anddecrease influence of the force equations on the fluid velocityestimate, as a degree of certainty that the speed of the fluid along thethird dimension is zero, decreases.
 5. The method of claim 3,comprising: adjusting the weighting based on a distance between thefirst object and the surface of the earth.
 6. The method of claim 1,further comprising: determining an orientation of the first object withrespect to a velocity of the first object relative to the fluid, basedon a velocity of the first object relative to the second object, anorientation of the first object with respect to the second object, andthe determined velocity of the fluid relative to the second object. 7.The method of claim 1, wherein: the velocity of the fluid relative tothe second object is a three-dimensional vector; the acceleration is athree-dimensional vector; and the thrust vector is a three-dimensionalvector.
 8. The method of claim 7, wherein the velocity of the fluidrelative to the second object is determined based on a mass of the firstobject, a reference area of the first object, and aerodynamiccoefficients of the first object.
 9. The method of claim 8, wherein theaerodynamic coefficients include an aerodynamic coefficient along eachaxis of the first object.
 10. The method of claim 1, wherein the stepsof determining the acceleration, determining the dynamic pressure, anddetermining the thrust vector are performed based on acceleration,dynamic pressure, and thrust data gathered when the first object has asteady state pitch angle of attack relative to the fluid and a steadystate yaw angle of attack relative to the fluid.
 11. The method of claim1, wherein the second object has a fixed position relative to the earth.12. A method for estimating air velocity of a vehicle, comprising:determining a parameter associated with the vehicle; and determining aweighting factor to weight force equations and a velocity equation in anequation set, based on the determined parameter; and solving theweighted equation set to estimate the air velocity of the vehicle. 13.The method of claim 12, wherein the parameter indicates a probability ofvertical velocity of the air with respect to a surface of the earth. 14.The method of claim 13, wherein the parameter corresponds to an altitudeof the vehicle above a surface of the earth.
 15. The method of claim 13,wherein the vehicle comprises an engine and the force equations describethrust force of the engine and aerodynamic forces acting on the vehicle.16. A device for estimating, at a first object in a fluid, a velocity inthree dimensions of the fluid relative to a second object, comprising: acomputer arranged to perform the steps of claim
 1. 17. The device ofclaim 16, comprising: at least one of an Inertial Navigation System anda Global Positioning System, connected to the computer to provide aposition of the first object relative to the second object.
 18. Thedevice of claim 16, wherein the computer is arranged to perform the stepof claim
 2. 19. The device of claim 16, wherein the computer is arrangedto perform the step of claim
 3. 20. The device of claim 16, wherein thecomputer is arranged to perform the step of claim
 4. 21. The device ofclaim 16, wherein the computer is arranged to perform the step of claim5.